Which equation represents the axis of symmetry of the function y = – 2x2 + 4x –6?
(1 point)
y=1 x=1 x=3 x = –3
x = 1
What are the coordinates of the vertex of the graph of the function y = –x2 + 6x –11?
(1 point)
(3, –2) (3, 16) (–3, –29) (–3, –20)
The vertex of the function y = -x^2 + 6x - 11 can be found by completing the square or using the formula x = -b/2a in the standard form of the quadratic equation, which is ax^2 + bx + c.
For the function y = -x^2 + 6x - 11, we have a = -1 and b = 6.
Using the formula x = -b/2a:
x = -6 / 2(-1)
x = -6 / -2
x = 3
To find y, substitute x = 3 back into the equation:
y = -(3)^2 + 6(3) - 11
y = -9 + 18 - 11
y = -2
Therefore, the coordinates of the vertex of the graph are (3, -2). So, the correct option is:
(3, –2)
What are the coordinates of the vertex of the graph of the function y = –3x2 –12x + 3?
(1 point)
(–2, 29) (2, –15) (2, –9) (–2, 15)
To find the coordinates of the vertex of the function y = -3x^2 - 12x + 3, we use the formula x = -b/2a in the standard quadratic equation ax^2 + bx + c.
For the function y = -3x^2 - 12x + 3, we have a = -3 and b = -12.
Using the formula x = -b/2a:
x = -(-12) / 2(-3)
x = 12 / -6
x = -2
To find y, substitute x = -2 back into the equation:
y = -3(-2)^2 - 12(-2) + 3
y = -3(4) + 24 +3
y = -12 + 24 + 3
y = 15
Therefore, the coordinates of the vertex of the graph are (-2, 15). So, the correct option is:
(-2, 15)